Nitrogen fertilization for cereal crop production does not follow any kind of
generalized methodology that guarantees maximum nitrogen use efficiency (NUE).
The objective of this work was to amalgamate some of the current concepts for
N management in cereal production into an applied algorithm. Our work at
Oklahoma State University from 1992 to present has focused primarily on the
use of optical sensors in red and near infrared bands for predicting yield,
and using that information in an algorithm to estimate fertilizer
requirements. The current algorithm, WheatN.1.0, may be separated into
several discreet components: 1) mid-season prediction of grain yield,
determined by dividing the normalized difference vegetative index (NDVI) by
the number of days from planting to sensing (estimate of biomass produced per
day on the specific date when sensor readings are collected); 2) estimating
temporally dependent responsiveness to applied N by placing non-N-limiting
strips in production fields each year, and comparing these to the farmer
practice (response index); and 3) determining the spatial variability within
each 0.4m2 area using the coefficient of variation (CV) from NDVI
readings. These components are then integrated into a functional algorithm to
estimate application rate whereby N removal is estimated based on the
predicted yield potential for each 0.4m2 area and adjusted for the
seasonally dependent responsiveness to applied N. This work shows that yield
potential prediction equations for winter wheat can be reliably established
with only 2-years of field data. Furthermore, basing mid-season N fertilizer
rates on predicted yield potential and a response index can increase NUE by
over 15% in winter wheat when compared to conventional methods. Using our
optical sensor based algorithm that employs yield prediction and N
responsiveness by location (0.4m2 resolution) can increase yields
and decrease environmental contamination due to excessive N fertilization.

INTRODUCTION

From the early 1950s to the early 1970s,
increased food production was a priority in agricultural areas around the
world (1). During this time period, the largest increase in the use of
agricultural inputs was for nitrogen (N) fertilizer, because it had the
largest impact on yield. Since the early 1960s, the increase in fertilizer N
consumption has continued, becoming somewhat stable over the past 10 years.
Although fertilizer N consumption and cereal grain production have both
increased over the last 5 decades, contamination of surface and groundwater
supplies continues because the efficiency at which fertilizer N is used in
grain production has remained at a stagnant 33% worldwide (2). While only 33%
of the nitrogen applied in fertilizer is recovered in the cereal grain
harvest, few published reports have documented practices which significantly
improve the efficiency at which N is used in cereal production.

Voss (3) noted that the greatest recent
improvement in fertilizer recommendations in many states was the calibration
of a soil nitrate test on which to base fertilizer N recommendations for corn
(Zea mays L.). Makowski and Wallach (4) showed that models including
end-of-winter mineral soil N gave more profitable N fertilizer
recommendations, but that 10 site-years of data were required for model
parameter estimation. It should be noted that wide spread adoption of soil
testing remains limited in both the developed and developing world. In
Oklahoma, annual soil testing takes place on less than 10% of the agricultural
land, and this number is significantly less in the developing world (Hailin
Zhang, Head of OSU Soil Testing Lab, personal communication, August 2003).

Various researchers have worked to predict N
mineralized from soil organic matter which could lead to improved N fertilizer
recommendations (5). Recent work by Mulvaney et al. (6) found that the
concentration of amino sugar N was highly correlated with check-plot yields
and fertilizer N response. Amino sugar N was determined on 5 gram soil
samples treated with 20 ml of 6M HCl heated under reflux (110-120°C) for 12
hours. The hydrolysis mixture was then filtered and stored at 5°C.
Neutralized (use of 1 M NaOH until a pH of 6.5 to 6.8 was achieved)
hydrolysates were analyzed for hydrolysable N, NH4-N and amino
sugar N using the diffusion methods described by Mulvaney and Khan (7). This
methodology successfully partitioned N-responsive from non N- responsive corn
for sites that received normal rainfall. It is not clear how this technique
could be implemented for within-season N fertilizer recommendations, because N
availability is strongly influenced by temporal changes.

Current strategies for winter wheat in Oklahoma
recommend that farmers apply 33 kg N ha-1 for every 1 Mg of
anticipated wheat yield (2 lb N ac-1 for every bushel of expected
wheat grain yield) they hope to produce, subtracting the amount of NO3-N
in the surface (0-15 cm) soil profile (8). When grain yield goals are applied
using this strategy, the risk of predicting the environment (good or bad year)
is placed on the producer, especially when farmers take the risk of applying
all N preplant. Schmitt et al. (9) reported similar recommendations of 20 kg
N ha-1 for every 1 Mg of corn (1.2 lb N ac-1 for every
bushel of corn) minus soil test NO3-N and/or any credits from
previous leguminous crops in the rotation. To some extent, university
extension (e.g., soil testing), fertilizer dealers, and private consulting
organizations have historically used grain yield goals, due to the lack of a
better alternative, and because producers have been able to relate to an
input/output strategy for computing N requirements.

Many researchers have used measurements of NO3-N
in plant tissue to identify N sufficiency or deficiency at early growth stages
in winter wheat (10). However, the utility of this approach was limited since
critical tissue NO3-N levels varied as a function of temporal
variability (11). Even so, petiole NO3-N has been successfully
used in potatoes, where monitoring NO3-N late in the season
provided a mechanism for improving quality in a region where irrigation was
used and temporal variability was limited (12).

Vaughan et al. (13) applied a combination of
improved spring fertilizer recommendations in winter wheat by using both total
N in wheat plant tissue and soil NH4-N to improve spring N
fertilizer recommendations in winter wheat and was able to prevent over
fertilization. Work in Pennsylvania by Fox et al. (14) found that stalk NO3-N
test taken two weeks after corn had reached physiological maturity was an
excellent indicator of corn N status. A critical level of 250 mg kg-1
separated N-sufficient from N-deficient sites. This same work showed that
chlorophyll meter readings at one-fourth milk line growth stage could be used
as a good indicator of corn N status, but was less reliable if
drought-stressed sites were included. In Nebraska, Varvel et al. (15) found
that chlorophyll meter readings and end-of-season stalk NO3-N
concentrations (threshold of 2000 mg kg-1) provided additional
criteria to help partition and separate fields into areas with potentially
different levels of residual soil N. They proposed that this information could
be used to guide soil sampling and to develop or improve site- specific N
fertilizer recommendations, which should decrease environmental risk by
reducing the amount of NO3-N available for leaching. Further
inspection of the Nebraska data showed that any time stalk nitrate levels were
in the 250 mg kg-1 region (retro evaluation versus the Fox et al.,
2001 data), grain yields were less than maximum (Gary Varvel, personal
communication, July 2003).

Wood et al. (16) found that tissue N
concentration at V10 and mid-silk were good predictors of corn grain yield,
noting that field chlorophyll measurements using a SPAD-502 chlorophyll meter
(Minolta Camera Co., Ltd., Japan) were highly correlated with tissue N
concentrations at both of these growth stages. Sensor work by Blackmer et al.
(17) indicated that the measurement of light reflectance near 550 nm had
promise as a technique to detect N deficiencies in corn leaves. Varvel et al.
(18) employed chlorophyll meter readings to calculate a sufficiency index
(as-needed treatment/well-fertilized treatment) whereby in-season N fertilizer
applications were made when index values were below 95%. If sufficiency index
values were below 90% at the V8 growth stage in corn, maximum yields could not
be achieved with in-season N fertilizer applications. This suggested that
pre-V8 N management was critical for corn.

Fiez et al. (19) reported on the need to reduce
N losses and lower N rates in winter wheat production, especially on
north-facing back-slopes. Lengnick (20) suggested that plant indicators
followed changes in landscape features that influenced biomass production and
N uptake. He speculated that these changes would not be revealed by soil test
analyses. Voss (3) suggested that a regional research approach using current
and potential precision agriculture technology could provide a large and
up-to-date data base on which to base nutrient recommendations across a wide
spectrum of soils and crops. This work further noted the importance of
simultaneously using soil and plant productivity indicators to make site
specific crop production decisions. The resolution at which these existed was
not addressed.

Raun et al. (21) showed that yield potential
could be estimated from mid-season sensor reflectance measurements (Feekes 4
to 6) in winter wheat. Their work employed the normalized difference
vegetative index (NDVI) computed from red and near infrared reflectance values
[NDVI = (NIR-Red)/(NIR+Red)]. NIR and Red are the reflectance measurements in
the near infrared and red bands, respectively. This work predicted yield
using the sum of two post dormancy sensor readings (NDVI) divided by the
cumulative growing degree-days or GDD ((Tmin + Tmax)/2-4.4°C) from the first
to the second readings. Tmin and Tmax are the minimum and maximum
temperatures in a 24 hour period. Their index, in-season estimated yield, or
INSEY was later modified whereby a single NDVI measurement was divided by the
number of days from planting to sensing, counting only those days where GDD >
0 (22). This method eliminated those days where growth was not possible as a
function of temperature, regardless of the soil moisture conditions. Raun et
al. (22) showed that N fertilization based on mid-season estimates of yield
potential increased NUE by more than 15% when compared to traditional
practices which applied N at uniform rates. A significant key to the success
of this work was collecting sensor readings from each 1m2 area and
fertilizing each 1m2, recognizing that the differences in yield
potential and subsequent fertilizer need exists at this spatial scale. This
spatial scale was determined in earlier work, where extensive soil sampling,
optical sensor measurements of plants, and geostatistical analyses, showed
that significant differences in N availability existed at a 1m2
spatial resolution and that each square meter needed to be treated
independently to maximize benefits (23, 24). Earlier work by Solie et al.
(25) noted that the fundamental field element for sensing and treating
fertility differences is that area which provides the most precise measure of
the available nutrient where the level of that nutrient changes with distance.

Taylor et al. (26) evaluated the relationship
between the coefficient of variation (CV) from grain yields and plot size.
This work showed that CVs decreased with corresponding decreases in plot
sizes. This research suggested that the small plot sizes were consistent with
the resolution where detectable differences in soil test parameters existed
and should be treated independently. Research conducted at the International
Maize and Wheat Improvement Center (CIMMYT) suggested that the use of within
row CVs in corn could be used to detect the physiological growth stage when
expressed spatial variability was the greatest from readings collected on a
daily basis throughout the growth cycle (27).

Over an eleven-year period, the authors have
developed a process to determine N fertilizer application rate from optically
sensed reflectance measurements that vary temporally and spatially. The
objective of this paper is to describe and justify that process.

MID-SEASON NITROGEN FERTILIZATION ALGORITHM

Rationale for Basing Algorithm on Predicted
Yield

In the last century, yield goals have provided
one of the more reliable methods for determining pre-plant fertilizer N rates
in cereal production. The logic of this approach makes sense, since at any
given level of yield for a specific crop, nutrient removal can be estimated
based on known concentrations in each respective grain. For example, total N
concentrations in wheat, corn, and rice grain average 2.13, 1.26, and 1.23 %N,
respectively (28). Although there are expected differences in
varieties/hybrids and growing conditions, these can be accurately estimated
for selected production regions and cultivars. Once expected removal amounts
are known (based on a projected yield), mid-season application rates are
determined by dividing removal by the projected use efficiency. Similarly,
known quantities of P, K, S, and other micronutrients within particular cereal
grain crops have been published by the Potash Phosphate Institute (Norcross,
GA) (29), and based on these concentrations, mid-season nutrient rates could
be determined at specific foliar nutrient application efficiencies.

Johnson (30) suggested that it is usually
advantageous to set the grain yield goal above that of average yields in order
to take advantage of above-average growing conditions when they are
encountered in dryland agriculture. Dahnke et al. (31) reported that yield
goal was the yield per acre you hope to grow, clearly delineating the risk
farmers take when applying preplant N. Work by Rehm and Schmitt (32)
suggested that with favorable soil moisture at planting it would be smart to
aim for a 10 to 20% increase over the recent average when selecting a grain
yield goal. They also indicated that if soil moisture was limiting, yield
goals based on past averages were not advisable for the upcoming crop. This
is an important observation, since the strategy proposed in this paper could
theoretically adjust mid-season projected yield goal or yield potential based
on soil profile moisture at planting, or better yet, profile moisture at the
time of sensing. This is consistent with observations by Black and Bauer (33)
who noted that grain yield goal should be based on how much water was
available to the winter wheat crop from stored soil water to a depth of 1.5 m
in the spring plus the anticipated amount of growing season precipitation.

Oklahoma State University Procedure and Algorithm for Calculating Spatial and
Temporal Varying N Fertilizer Rates

The Oklahoma
State University optical sensor based algorithm calculates N fertilizer rates,
and it depends on making an in-season estimate of the potential or predicted
yield, determining the likely yield response to additional nitrogen
fertilizer, and finally calculating N required to obtain that additional
yield. In addition, a procedure has been developed to modify the calculated
fertilizer response to account for the effect of spatial variation as it
affects the crops ability to respond to additional fertilizer. Our approach
is based on the ability to predict yield potential and to calculate N required
based on the total amount of a given nutrient that will be removed in each
crop.

1. Estimate of Yield Potential

Work by Stone et al. (34) showed that
early-season NDVI readings of winter wheat measured with an optical sensor
were highly correlated with total above ground plant biomass. The effect of
the number of days of active plant growth prior to sensing was minimized by
dividing NDVI readings by the number of days from planting to sensing where
GDD > 0. Including only those days where GDD was more than 0 was necessary in
order to remove days where growth was not possible in winter wheat, and which
were notably variable over sites and years. In essence, the index, INSEY, was
an estimate of biomass produced per day when growth was possible. Raun et al.
(22) showed that optical sensor readings could be collected once, anytime
between Feekes growth stages 4 and 6, and that INSEY was an excellent
predictor of yield (grain or forage depending on the system). This work was
recently updated to include 30 locations over a 6-year period from 1998 to
2003 (Figure 1).

What is striking
from this research is that planting dates ranged from September 24 to December
1 (difference of 68 days), and sensing dates ranged from February 10 to April
23 (difference of 72 days), (range of differences from planting to sensing of
133 to 184 days) yet yield prediction remained quite good (solid line). The
results clearly indicated that, for winter wheat, biomass produced per day was
an excellent predictor of grain yield. Furthermore, over this 6-year period,
5 different varieties (Tonkawa, 2163, Custer, 2137, and Jagger) were included
in this database (Table 1). In this regard, it was noteworthy to find such a
good relationship with final grain yield, because so many uncontrolled
variables from planting to sensing (rainfall, planting date, temperature,
etc.) had the potential to adversely affect this relationship. The good
correlation was somewhat surprising when considering the many post-sensing
stresses that could be encountered, and would decrease yields (rust, drought,
weed infestations, etc.). These unpredictable by-site problems would
undoubtedly decrease correlation, since all experimental sites were included
in the database. Furthermore, considering the many post sensing conditions
that could impact the relationship between INSEY and final grain yield, the
relatively good fit of the exponential curve in Figure 1 (solid line) strongly
supports the argument that yield potential can indeed be predicted. However,
that potential may not be realized because post-sensing conditions could
adversely impact final grain yield.

Because of the importance of yield potential for
determining N application rates, we must expand the concept. The yield
potential for any given 0.4m2 area is the grain yield achievable,
considering total plant growth from planting, accounting for plant stand
and/or damage on the date of sensing. The same spot will likely have the same
yield potential whether or not it was sensed on March 1, or March 10 for a
given year, since days from planting acts as the normalized divisor. The
relationship between yield data and sensor data can be described by an
exponential curve. However, standard regression techniques produce a
prediction model that includes data from fields whose yields were adversely
affected by events subsequent to the date of sensing that could not be
predicted. Consequently, a model of actual grain yield will under predict or
over predict potential grain yield at the sensing date. To correctly predict
the potential yield, the model should be fitted to yields unaffected by
adverse conditions from sensing to maturity. Since actual yields include some
that were reduced by poor growing conditions after sensing, and some that were
not, it is important to use the actual yields unaffected by post sensing
factors when predicting potential yield.

There is currently no established empirical
method to determine how much the curve should be shifted. We have elected to
adjust the constant a within the exponential model (y = aebx)
such that the number of observations above the curve was 32% of the total data
points (Figure 1.). This curve more realistically represents the yield
potential achievable in rainfed winter wheat considering that post-sensing
stresses (moisture, disease, etc.) from February to July could lower observed
yields. Thus, yield potential or YP0 + 1 standard deviation is
currently used in our algorithm for predicting yield potential. The model
currently used to predict wheat grain yield is:

(1)

It is of further importance to note that
differences from yield prediction equations formulated using the first 2 years
(1998-1999, 8 locations), second 2 years (2000-2001, 12 locations), and third
2 years (2002-2003, 10 locations) of field data, did not differ substantially
when compared to each other (Figure 2). This suggests that it is possible to
establish reliable yield potential prediction from only 2 years of field data,
provided that enough sites were evaluated within this time period. Regression
significance (R2) differed among the 3, 2-year data sets, which was
expected, but with very small differences between regression coefficients.
For all the 3, 2-year data sets, outer limits (left edge of the points from
each 2-year data set moving from left to right) did not change substantially,
and the equations were quite similar to that found for the 6-year model
(Figures 1 and 2).2. Estimating the Responsiveness to Applied N

Identifying a specific yield potential does not
translate directly to an N recommendation. Determining the extent to which
the crop will respond to additional N is equally important. The concept of
the response index (RI) was expanded from initial work by Johnson and Raun
(35) to predict crop response to additional N fertilizer using in-season
sensor measurements (36). The Response Index is defined as:
(2)
Where: RIHarvest is the fertilizer Response
Index for a harvested crop.YldNRich is the grain yield from an
area treated within sufficient N fertilizer to
assure that N is non-limiting.YldFieldRate is the grain yield from
an adjacent area treated at the normal field
N application rate.
RI varied from field to field and over years and likely varied spatially
within a field. To determine RI, N fertilizer was applied to a strip
extending across a field at a rate sufficient to assure that N was not
limiting, but not excessive (Nitrogen Rich Strip). Midseason estimates of
RIHarv were made by optically scanning the growing crop and
calculating the NDVI response index, RINDVI:
(3)
Where: NDVINRich is NDVI of an area within the
NRich stripNDVIFieldRate is NDVI of an adjacent
area treated at the normal N rate.

This fertilizer index was developed following
comprehensive work by Johnson and Raun (35) demonstrating that the response to
applied N in the same field is entirely variable from one year to the next and
independent of whether or not previous year yields were high or low. They
studied grain yield response to applied N in a long-term replicated experiment
where the same rates were applied to the same plots each year for over 30
years. The response to applied N changed drastically from one year to the
next, with the check plot yield (no N applied over this 30+ year period)
showing no consistent trend to decline (Figure 3). This was attributed to N
mineralization and variable N contributions from the atmosphere and rainfall
that were unpredictable over time and dependent on highly variable weather
conditions (35).

Because the response to N fertilizer is
dependent on the supply of non-fertilizer N (mineralized from soil organic
matter, deposited in the rainfall, etc.) in any given year, N management
strategies that include a reliable mid-season predictor of RI should
dramatically improve NUE in cereal production (35). This paper noted that the
RI values changed considerably when collected from the same plots that had
been managed the same way for 30 years. This was attributed to the striking
differences in rainfall and temperature from one year to the next and
associated crop need (temporal variability), which influenced how much
non-fertilizer N was used by the crop.

The relationship between RI computed from NDVI
readings collected from the check plots and adequately N fertilized plots at
Feekes growth stages 4 to 6 (RINDVI) with RI computed from
harvested grain (grain yield ratio determined from the same respective plots,
RIHarv) over 63 locations from 1998 to 2003 is reported in Figure
4. RINDVI was positively correlated with RIHarvestover this 6-year period. However, RINDVI could
greatly underestimate the benefits of additional N fertilizer particularly in
the middle range. The improved fit of a linear-linear curve in this middle
region indicated that RINDVI measurements in midseason could
not fully account for intervening causes improving final yield. Despite this
limitation, RINDVI has proven to be a good, conservative
predictor of wheat grain yield with additional fertilizer.

Where RINDVI is used to
predict the average grain yield response to additional fertilizer, average
NDVI of the NRich strip should be compared with average NDVI of a field rate
strip immediately adjacent to the NRich strip. Where RINDVI
is used to predict spatially varying response within a field, NDVI
measurements should be made in an area where observation indicates that
response to fertilizer is high.

The highest NDVI measurement along the NRich
strip can be used to calculate (Equation 1) the maximum potential yield.
YPmax is the maximum yield that could be expected within the
most productive area in a field when N was not limiting for the year of
measurement.

The boundaries circumscribing potential yield
with and without additional fertilizer are the curves predicting potential
yield without additional fertilizer (YP0), potential yield with
additional fertilizer (YPN), the maximum expected yield and a
cutoff for areas with few or no wheat plants (transition from soil to
plants). The potential yield without additional fertilizer, YP0,
can be calculated directly by equation 1.

(4)
The following equations predict the potential yield with additional N
fertilizer, YPN:

(5a)

Or

(5b)

Observations over several years indicate that values of NDVI < 0.25 occur on
bare soil or on soil with wheat stands so poor at Feekes 5 that they will not
produce appreciable yields.

Examination of Figure 5 illustrates the critical
points of the RI theory for predicting yield increase. Below field rate NDVI
= 0.25, when measured after 120 days of active plant growth, crop potential
yield is considered low enough that there are no appreciable benefits in
adding additional N. This is the transition from bare soil to wheat. In this
example, between NDVI = 0.25 and NDVI = 0.57 the crop benefits from additional
N, and the potential yield increase is the product of RI and potential yield
without additional N, YP0. Between NDVI = 0.57 and NDVI = 0.73,
additional fertilizer can boost grain yield up to the maximum potential yield,
YPmax. Beyond NDVI = 0.73 there is no benefit for additional
fertilizer N, because potential yields have reached the maximum for the field.

The RI theory for predicting yield increase with
additional N has one additional consequence. Increasing the value of RI
causes YPN to more rapidly reach YPmax (Figure 6). This
causes the division point separating the region where the response index
controls YPN from the region where YPmax limits YPN
to shift to lower values of NDVI. At its extreme, where RINDVI =
4.3, the crop yield at any location in the field and NDVI ³
0.25 can be raised to the maximum yield.

The topdress N requirement can be calculated by:

(7)

Where: R is
the N application rate, kg/ha

23.9 is the decimal percentage of N by weight
contained in wheat grain multiplied by a
conversion constant

h
is an efficiency factor, 0.5 £h£
0.7

Plots of equation (7) for response indices of 1.25, 1.75, and 2.5 illustrate
the effect of the RI on the nitrogen application rate (Figure 7). The maximum
N application rate for RI = 1.25 was 23.7 kg ha-1, and the peak
value did not occur until the field rate NDVI reached 0.70. As RI increased
to 2.5, the peak N application rate increased to 72.4 kg ha-1, and
the peak application rate occurred at a much lower value of field rate NDVI,
0.45. For the conditions of YPmax = 3 Mg ha-1
and 120 days after planting where GDD > 0, RI
would equal 4.3, the N application rate equals 92.9 kg ha-1, and
the peak application rate occurs at NDVI equals 0.25. In that case, only N is
the limiting factor.

Validation of
the Oklahoma State University Optical Sensor Based Algorithm for Crop
Nitrogen Fertilization occurs at two levels, paired comparisons of estimated
yield from NRich and adjacent field rate fertilizer strips and an extensive
series of field trials testing the algorithm. Solie et al. (2004) (reference
not included) examined 16 N Rich strips sensed with either the GreenSeekerTM
sensor or IKONIS satellite imagery. For the IKONIS imagery, NDVI was
calculated for paired pixels in the N Rich strip and the adjacent field rate
area. Pixel size was 4 by 4 m and paired data were separated by one pixel, 4
m. An examination of the data compared with the imagery showed that
aberrations in the form of spikes in RINDVI occurred whenever the
NRich strip crossed a terrace. These spikes occurred because of the
relatively large pixel size and the fact that data pairs were separated by 4 m
and NDVI values changed between the backside and channel of the terraces. The
result was no relatedness between paired measurements. Data in the vicinity
of terraces were deleted. Potential yield was calculated for data from the
NRich strip. YPNRich data were plotted in Figure 8 along with the
YP0, YPN, YPmax and Soil/Plant transition
curves as a function of field rate NDVI. The YPN curve was
calculated using the maximum value of RINDVI along the strip, RINDVI
= 1.37.

All data fell on or below the YPmax
cap, but Nrich potential yield data paired with field rate NDVI measurements
³
0.52 were clustered closely in the vicinity of the cap. The few measurements
falling below the YP0 boundary were a consequence of the limited
relatedness that could occur when measurements separated by 4 m were use to
calculate RINDVI. In these instances, RINDVI < 1. As
noted previously, RINDVI provided a conservative estimate of NDVI
with a number of YPNRich data points paralleling the YPN
curve but with values greater than predicted by RINDVI. To
overcome the problem of underestimating potential yield, an alternative
response index based on potential yield was formulated, RIYP:

(8)

A
curve calculated with RIYP = 1.58 (the greatest difference of NDVI
and INSEY between data pairs) bounded all data and passed through the maximum
value of YPNDVI in the region where RI defined YPN.
This NRich strip as well as the other 15 NRich strips, were examined by Solie
et al. (2004) confirmed the theory that potential yield with additional N
could be increased by the product of YP0 measurement times the
response index in the region where the response index set the boundary. At
higher levels of NDVI, all treated areas could be raised to a cap, YPmax.

Over the last five years, an extensive series of
field trials have been conducted to test the Optical Sensor Based Algorithm
for Crop Nitrogen Fertilization. Results of these experiments have supported
the validity of the theory and these have been reported at
http://www.dasnr.okstate.edu/nitrogen_use.

Adjusting RI for Reduced or Increased
Response to Nitrogen

Evaluation of results testing the Optical Sensor
Based Algorithm for Crop Nitrogen Fertilization and the NRich strip have shown
that there are regions in the field where the response to additional N is less
than or occasionally greater than predicted by the algorithm.

Measuring the variability in plant stand and growth at high resolution, less
than 0.4 m2, in farmer fields can enable us to adjust the response
index for mid-season N fertilization in grain crops. In general, this small
area spatial variability can be estimated by the coefficient of variation (CV)
of high resolution measurements of NDVI. CV has been shown to be highly
correlated with plant population within each 0.4m2 area. NDVI is
well correlated with N uptake (34), and since N uptake is the product of N
content and plant biomass (plant population), it follows that estimates of N
uptake will be improved by identifying changes in plant population and plant
growth. Because of this relationship, we can decipher more about the
potential yield obtainable with added N fertilization than by an average value
of NDVI within the sensed and treated area. If plant stands and growth are
irregular (high CV), the potential yield with added N fertilization, RI, will
be lower than if plant stands are uniform (low CV) with the same mean NDVI.
On-the-go monitoring of the NDVI coefficient of variation offers the potential
to improve our calculation of N fertilizer rate.

The ability to accurately measure CVs on-the-go
is also a function of the sensors employed. The sensors developed by Oklahoma
State University and currently sold by NTech Industries (Ukiah, CA) collect
many individual readings (>10 in each 0.4 m2 traveling at 10 mph).
No other precision agricultural technology being developed today can collect
as many comprehensive readings on such a small scale, and on-the-go. Work by
Taylor et al, (37) indicated that 15 to 16 readings from each area of interest
were required to obtain a reliable composite soil sample. The 10 readings
collected from each 0.4 m2 used here were considered to be
sufficient to obtain a composite sample from such a small area, understanding
that the 10 sensor readings were representative of each 0.4 m2
surface area. The resultant CV from the area of interest is representative of
the variability from the same 0.4 m2 area, not just a small portion
as would be the case with chlorophyll meters. Clearly, plant stands should be
expected to vary at the same scale for which they are planted, which is by
seed in corn.

Over the last two years, high frequency
measurements of NDVI were made and wheat yields collected at 1 m2
resolution (Figure 9). These data show a definite relationship between CV
within a plot and grain yield, despite the scatter in data. An equation (Eqn.
9) relating the response index to the coefficient of variation can be derived
the linear model for CV  wheat yield data:

(9)

Dividing by the average yield at CV = 0, YPCV0
gives:

(10)

When measured in the field, NDVIFldRate always has a CV > 0.
Equation 11 can be used to calculate the intercept RICV0:

(11)

Where RIMax is the maximum response index along the NRich strip and
CVMaxRI is the CV of the field rate NDVI used to calculate RIMax.

Predicted yield using RICV , YPCV, is calculated by
equation 12:

(12)

These equations hold for RINDVI, RIYP, or any other
response index predicting increased yield with additional fertilizer N. The
effect of CV on the response index is similar to that seen with changes in
measured RI (Figure 10). Although CV of wheat used to calculate YPmax
is generally very low, there can be instances when yields predicted using RICV
are greater than YPmax.

DISCUSSION

If the resolution where significant differences
in biological properties (plant or soil) were found at 0.4 m2, that
same resolution would be where recognizable differences in statistical
properties could be discerned as well. Nutrients can vary at different scales
for different reasons. Variability at the finest scale encompasses all
causes. At coarser scales, we average out some of the cause for variability.
Spatial variability of soil nutrients has already been established for a
resolution scale of 0.4m2. Therefore, variability among 0.4m2
areas is a function of nutrient availability, whereas variability within 0.4m2
is likely a function of crop conditions other than nutrient availability.
Furthermore, it should be noted that plants and their roots integrate nutrient
variability that can exist within each 0.4m2, but that is not
expressed because plant uptake and/or growth will average whatever variability
might be present at that scale.

Although CVs from small yield potential plots
assisted in removing some of the variation in predicted yield when combined
with INSEY (in season estimated yield), this approach is flawed since the CV
needs to be applied to the response index for added N fertilization.
Adjusting RI as a function of CV can account for the inability to reach the
yield predicted by RI or maximum potential yield,YPmax.

The yield potential obtainable without added N
fertilization (YP0) for a minimum sized field element should be
independent of CV. This was confirmed when evaluating the relationship
between CV determined from NDVI readings taken between Feekes 4 and 6 over 21
locations from 2000 to 2003, and where yield data were also collected from 1m2
areas (Figure 6). Although there was a trend for grain yields to decrease
with increasing CV, correlation was poor.

Unlike YP0, the yield potential
obtainable with added N fertilization (YPN) should be dependent on
CV. While actual yield level with no added inputs is independent of CV, the
yield level that can be achieved if changes or additions are made is directly
related to how much the level of variability existed within each 0.4m2
area. When CV is low, a responsive field element should be capable of greater
yield than when a similarly responsive field element CV is large. To test
this concept, observed grain yield obtained when added N fertilization
occurred after sensing was evaluated as a function of predicted yield using
INSEY and the coefficient of variation at the time of sensing in the equation
(YPN_CV). Predictive methods for determining YPN_CV
were delineated in the previous section. For all the plots reported in Figure
7, NDVI sensor readings were taken from winter wheat somewhere between Feekes
growth stages 4 and 6. Enough readings were collected from each plot to
determine the CV. Following sensor readings, N was applied at different rates
(varied by location and year) to achieve the yield potential estimated in the
RI-NFOA algorithm. CV data were not used to determine N application rates.
To evaluate the potential usefulness of CV for predicting the yield that could
be achieved with added N fertilization, actual yield, YPN and YPN_CV
were plotted for all 6 trials where these data were collected (Figure 11). YPN
clearly resulted in overestimating actual yields obtained, 5.5 Mg ha-1.
YPN_CV values more closely followed observed yield. When actual
INSEY values exceed 0.006, observed yield clearly reached a plateau or yield
maximum of 3.0 Mg ha-1. Although the current YPN_CV
formula employed resulted in a plateau at somewhat higher INSEY values (0.008)
than with observed yield (0.006), it predicted a yield plateau.

The need to sense biological properties on a
small scale (0.4m2 or smaller) was established by Solie et al.
(24). Not until recently did we consider the evaluation of statistical
properties within each 0.4m2, understanding that the variability
within each 0.4m2 would be associated with something other than
nutrient variability that would be minimal at this scale. Fortunately, the
sensors developed and used in all the Oklahoma State University Sensor
research are capable of collecting enough data within each 0.4m2 to
calculate meaningful statistical estimates at this small scale. Now, these
statistical estimates on each 0.4m2 can be combined with average
NDVI from the same 0.4m2 to better predict mid-season yield and
subsequent fertilizer N rate requirements.
Using the RI-NFOA algorithm reported earlier, Raun et al. (22) showed that
winter wheat NUE was improved by more than 15% when N fertilization was based
on INSEY calculated from optically sensed NDVI, determined for each 1m2
area, and the response index when compared to traditional practices at uniform
N rates. We are not aware of any biological basis to suggest that this
approach would not be suitable in other cereal crops.

Figure
1. Relationship between observed wheat grain yield and the In Season Estimated
Yield (INSEY) determined by dividing NDVI by the number of days from planting to
sensing (days where growth was possible, or GDD > 0) at 30 locations from 1998
to 2003.

Figure
2. Relationship between observed wheat grain yield and the In Season Estimated
Yield (INSEY) determined by dividing NDVI by the number of days from planting to
sensing (days where growth was possible, or GDD > 0) using 8 locations from 1998
to 1999, 12 locations from 2000 to 2001, and 10 locations from 2002-2003.

Figure
4. Relationship between RINDVI and RIHarvest from 63
winter wheat experiments, 1998 to 2003, central and western OK.

Figure
5. Change in potential yield of wheat with additional N fertilizer for a
Response Index of RI = 1.5, a maximum potential yield of 3.0 Mg ha-1
and 120 days after planting where GDD > 0.

Figure
6. Shift in portion of the YPN curve for changes in the Response
Index, RI, where YPmax serves as the upper boundary for potential
yields from additional N fertilizer for a maximum potential yield of 3.0 Mg ha-1
and 120 days after planting where GDD > 0.

Figure
8. Potential yield from 4 by 4 m areas within the NRich strip (NRich YP)
plotted as a function of NDVI of paired areas in the adjacent field rate strip
bounded by the curve of: potential yield with no additional N (YP0),
the cap or plateau of maximum yield (YPmax), the transition from bare soil to
viable crop, and the product of YP0 and either RINDVI or
RIYP. Data from IKONIS imagery of a wheat farm near Covington, OK.

Figure
9. Relationship between observed grain yield and the coefficient of variation
from sensor readings taken at early stages of growth (Feekes 4 to 6) in winter
wheat from 21 locations over a 3-year period, 2000-2003.

Fig. 10. The effect of
CV of high-resolution NDVI measurements on the response index and potential
wheat yield.